Since heraldry is mainly concerned with identifying individual persons, there cannot be said to be such a thing as a "Clan coat of arms." The arms shown here actually or potentially pertain only to the individuals they identify and should not be appropriated or used by others in any way.
However, among the MacGillivray arms which have been recorded in the Public Register of All Arms and Bearings of Scotland within the 20th century, a number of common and characteristic features are observable, most of them originating in the Arms of the Chief, shown below.

MacGillivray of DunmaglassCHIEF OF THE CLAN MacGILLIVRAYRecorded in the Public Register of All Arms & Bearings of Scotland, Court of Lord Lyon King of Arms14 October 1967.

Although armorial bearings were used by the MacGillivray chiefs of Dunmaglass and their kin as early as 1535, arms for a Chief were never officially recorded in the Public Register of All Arms & Bearings established by law in 1672. This remained the case up to the apparent extinction of the chiefly line in the 20th century.
The arms at left were matriculated in 1967 in favour of past chiefs--specifically Farquhar IV of Dunmaglass, who would have been Chief just after the establishment of the Register--by Col. George B. Macgillivray of Thunder Bay, Ontario, in connection with his own petition for the Chiefship, which was pending at that time. The source of this design is several armorial gravestones on the grounds of Dunlichity Church in Strathnairn, burialground of the Dunmaglass chiefs and their Strathnairn clansfolk.

Guidon, or Standard, of MacGillivray of Dunmaglass

Inasmuch as Col. Macgillivray did not succeed in acquiring the Chiefship and it remains vacant to this time, no one has ever personally borne these arms. They remain reserved for the use of a claimant to the Chiefship who may someday prove his right to them.The Guidon, shown below the Arms, is a Standard, or pennon-shaped flag, 8 feet in length, which is used to designate the Chief's headquarters on the field or at any suitable public event. In the hoist is the Chief's Arms as on his Shield, then a personal Badge, in this case a Cat grasping a sapling of Boxwood within a chaplet quartered green (vert) and gold (or), followed by the name of the Chiefs' traditional duthus, "Dunmaghlas," in the fly.Among the arms of clansmen (i.e., MacGillivray "armigers") which are on record in Scotland, especially those matriculated since the 1967 arms above, features in common with the Chiefly arms are easy to spot. This follows the pattern in Scotland of clansmen's arms referring to the arms of the Chief, as a signal of his pre-eminence in the Clan and their place as his followers.

Symbolism of the Arms
The meanings of the various charges in an achievement of arms can be difficult to track because they will be based on personal, historic and traditional references that may now be obscure. But most elements in the Dunmaglass arms, which are derived from the designs of armorial stones at Dunlichity, have reasonably clear significance.Clan Chattan charges.Several elements give witness to the MacGillivrays' well known status as an important consituent clan of the Clan Chattan tribal confederation. The Cat, a Highland wildcat, is the beast of Clan Chattan, found in the arms of many of the chiefs and clansfolk of the confederation. This is a "canting" charge, meaning it represents a visual pun on the name Chattan, actually derived from St. Cattan, but obviously resonant with the native feline of the Highlands, renowned for its fierce territoriality. The use of the Cat in the Crest, atop the Helmet, is common in Clan Chattan, but it is of interest that MacGillivray arms are the only ones to use it also as a charge on the Shield, in the first quarter. The Motto, "Touch Not This Cat", is a shortened version of the warning found in Mackintosh and MacPherson arms: "Touch Not the Cat Bot a Glove." Another Chattan charge is the Galley, or Lymphad, in the fourth quarter of the Shield, with a colour scheme of a blue (azure) ship on a gold (or) field, flagged and with crossed oars of red (gules), distinguishing it from the black (sable) galley found in the arms of the MacDonalds and other coastal clans. Unusual to this case, it is clearly sailing to the sinister.The Hand and the Salmon.Both of these charges seem to be references to the west coastal origins of the MacGillivrays, and perhaps to their antiquity. The red Hand upright, couped at the wrist and palmwise is said to be a heraldic "sign of valour and a symbol of faith and justice," perhaps even suggesting the judicial office of deemster that is thought to be the origin of the name. Upon its field of white (argent), the red hand's link to the ancient symbol of the northern Irish province of Ulster is almost too obvious to ignore, suggesting a belief that the MacGillivrays were among the original Gaels from thence who established the first kingdom of "Scots"--Dalraida--in the west around A.D. 500.The Salmon may have similar meanings, as an ancient Celtic totem of royalty and tenacity used by many of the clans of the west coast and Isles. A story from MacDonald tradition may have particular bearing here. It is said that in the 12th century, the MacGillivrays and other folk of Morvern called upon Somerled, son of Gillebride, to lead them in repelling the Norse raiders in the area. Somerled had been working for some time at landing a particularly fine salmon, and he promised that if he first succeeded, within that day, he would then take up their cause. The salmon was caught, and since has featured in the MacDonald arms, symbolising Somerled's status as Clan Donald's founder.The patch of ground beneath the Shield, the Compartment, is reserved to chiefs and others who have territorial authority. Growing from it are two shrubs of Boxwood, the traditional Plant Badge of the Clan.